On the estimation of trends in annual rainfall using paired guage observations

A method was recently proposed for evaluating the impact of a perturbation, such as air pollution or urbanization, on the precipitation at a location by calculating the ratio between the precipitation at the perturbed location and that at a location believed to be unperturbed. However, this method may be inappropriate because of the high degree of variability of precipitation at each of the stations. To explore the validity of this approach, noisy annual rainfall records are generated numerically in an upwind, unperturbed station and in a downwind, perturbed station, and the time series of ratio between the annual rainfalls in the two stations is analyzed. The noisy rainfall records are 50 yr long, and the imposed trend for the downwind, perturbed station is -2 mm yr^-1 while at the upwind station the variations in annual rainfall are purely noisy. Many pairs of noisy rainfall records are numerically generated (each pair constitutes an experiment), and in every experiment the slope of the linear best fit to the rainfall ratio yields an estimate of the trend of rainfall at the perturbed station. In the absence of noise, the trend of the rainfall ratio is explicitly related to the trend of rainfall at the perturbed station, but the natural rainfall variation at the stations completely masks this explicit relationship. The results show that in some experiments the trend line of the rainfall ratio has the opposite sign to the imposed trend and that in only about one-half of the experiments does the ratio's trend line lie within ±75% of the imposed trend. Trend estimates within ±25% of the imposed trend are obtained in less than one-quarter of the experiments. This result casts doubt on the generality and validity of using trends of rainfall ratio between two stations to estimate trends of precipitation in one of these stations.